Well T Rex did seem to be quite slow and I always thought that it was an opportunisting hunter/scavenger. I do doubt wether it could have hunted bison very well or other crafty mammals as it would have been so obvious in its approach (Bison live on plains).
Tyrannosaurus was not a fast runner | Nature
http://www.biomechanics.bio.uci.edu/..._biomech/trex/trx.htm
I think the biggest problem with dinosaurs co existing with modern creatures is the fact that they lay eggs on the ground. These would be a veritable storehouse of easy to access protien for egg eaters.
You also forget that people would have done there best to erradicate any hostile megafauna.
Megalania is a good example of a big ass monitor lizard that went extinct about 40000 BCE. This would have coexisted with the animals you mentioned. Now it's dead.
The thing is that there is no evidence that all these animals coexisted and if through some magic they did you would need climatic conditions that would favour each time periods organisms.
Drop a mammoth into the wrong time period and it dies. Do the same for other creatures and they die.
One way around the problem is to suggest that the climatic conditions of the ante-diluvian realm were very isolated in some way.
I have often wondered 'who would win' if dinosaurs were somehow pulled from the past and I think I concluded that the dinosaurs would 'win' in the short term but laying eggs on land would be the death of them.
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